Abstract
In our previous paper 4) -12), we have studied “Theory of Invariance” for nonlinear continuous-time systems with their inputs appearing linearly. The aim of this paper is to derive necessary and sufficient conditions that inputs never effect outputs (so called conditions of “Invariance”) for nonlinear discrete-time and continuous-time systems without the assumption of linearity in inputs. Applying these conditions to the decoupling problem, we obtained necessary and sufficient conditions which yield decoupling control laws for both the continuous-time systems and the discrete-time systems. The conditions of decoupling given by van der Schaft 13) and Grizzle 14) via geometric approach are different in forms from ours. But, it seems difficult to derive control laws from their conditions because the integration of partial deferential equations is needed there.
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